Transformational classes of grammars

Given two Chomsky grammars G and \-G, a homomorphism φ from G to \-G is, roughly speaking, a map which assigns to every derivation of G a derivation of \-G in such a manner that φ is uniquely determined by its restriction to the set of productions of G. Two grammars are contained in the same transformational class, if the one can be transformed into the other by a sequence of homomorphisms. If two grammars are related in such a manner, then there are two relations, one concerning the words of the languages generated and the other regarding the derivations of these words. We establish several classifications of context-free grammars in transformational classes which are recursively solvable

Graph automata

AbstractMagmoids satisfying the 15 fundamental equations of graphs, namely graphoids, are introduced. Automata on directed hypergraphs are defined by virtue of a relational graphoid. The closure properties of the so-obtained class are investigated, and a comparison is being made with the class of syntactically recognizable graph languages

Context-Free Grammars: Covers, Normal Forms, and Parsing

This monograph develops a theory of grammatical covers, normal forms and parsing. Covers, formally defined in 1969, describe a relation between the sets of parses of two context-free grammars. If this relation exists then in a formal model of parsing it is possible to have, except for the output, for both grammars the same parser. Questions concerning the possibility to cover a certain grammar with grammars that conform to some requirements on the productions or the derivations will be raised and answered. Answers to these cover problems will be obtained by introducing algorithms that describe a transformation of an input grammar into an output grammar which satisfies the requirements. The main emphasis in this monograph is on transformations of context-free grammars to context-free grammars in some normal form. However, not only transformations of this kind will be discussed, but also transformations which yield grammars which have useful parsing properties